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Preheat the oven to 400°F.
Remove and discard the loose outer leaves from the sprouts, and cut the sprouts in half through the core.
Put the bacon in a wide oven-safe sauté pan or skillet and cook over medium heat, stirring occasionally, until just about crisp, 5 minutes or so. With a slotted spoon, transfer the bacon to a paper towel-lined plate and reserve.
Drain off most of the fat from the pan and add the sprouts, cut side down. Raise the heat to medium-high and sear until the sprouts begin to sizzle. Put the skillet in the oven and roast until the sprouts are deeply browned, about 8 minutes, then shake the pan to redistribute them. Pull the pan from the oven when the sprouts are bright green and fairly tender (taste to check), 10 to 15 minutes more.
Return the pan to the stovetop over medium heat and stir in the butter, bacon, and salt, and pepper to taste. Toss the sprouts to coat them.
Place the kimchi in a large serving bowl. Use the back of a spoon to spread the kimchi out so it covers the bottom. Add the sprouts, arranging them in a tidy pile on top of the kimchi. Garnish with a pile of julienned carrots and serve.